which statement best explains the relationship between lines fg and hj?

they are perpendicular because their slopes are equal.
they are perpendicular because their slopes are negative reciprocals.
they are not perpendicular because their slopes are equal.
they are not perpendicular because their slopes are not negative reciprocals.

Question

which statement best explains the relationship between lines fg and hj?

they are perpendicular because their slopes are equal.
they are perpendicular because their slopes are negative reciprocals.
they are not perpendicular because their slopes are equal.
they are not perpendicular because their slopes are not negative reciprocals.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perpendicular Line Slopes" ], "new_concepts": [], "current_concepts": [ "Perpendicular Line Slopes", "Slope-Intercept Form" ] } ## Calculate the slope of line FG $$ \begin{aligned} &\text{Point } F = (-4, 1), \quad \text{Point } G = (-1, -1)\ &m_{FG} = \frac{-1 - 1}{-1 - (-4)} = \frac{-2}{3} = -\frac{2}{3} \end{aligned} $$ ## Calculate the slope of line HJ $$ \begin{aligned} &\text{Point } H = (-4, -2), \quad \text{Point } J = (-1, 3)\ &m_{HJ} = \frac{3 - (-2)}{-1 - (-4)} = \frac{5}{3} \end{aligned} $$ ## Determine the relationship between the slopes $$ \begin{aligned} &m_{FG} \cdot m_{HJ} = -\frac{2}{3} \cdot \frac{5}{3} = -\frac{10}{9} eq -1\ &-\frac{2}{3} eq -\frac{1}{5/3} = -\frac{3}{5} \end{aligned} $$

They are perpendicular because their slopes are equal.

They are perpendicular because their slopes are negative reciprocals.

They are not perpendicular because their slopes are equal.

They are not perpendicular because their slopes are not negative reciprocals.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Line Slopes" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the slope of line FG

Calculate the slope of line HJ

Determine the relationship between the slopes

Answer: